Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse x²/4 + y²/25 = 1

Solution:

The given equation is x²/4 + y²/25 = 1

Here, the denominator of y²/25 is greater than the denominator of x²/4

Therefore, the major axis is along the y-axis, while the minor axis is along the x-axis.

On comparing the given equation with x²/b² + y²/a² = 1 we obtain b = 2 and a = 5

Hence,

c = √a² - b²

= √25 - 4

= √21

Therefore,

The coordinates of the foci are (0, ± √21)

The coordinates of the vertices are (0, ± 5)

Length of major axis = 2a = 10

Length of minor axis = 2b = 4

Eccentricity, e = c/a = √21/5

Length of latus rectum = 2b²/a = (2 × 4)/5 = 8/5

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 2